Difference of Squares

Summary

Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.

Perfect Squares

A perfect square is a term that can be written as the product of a term with itself, or the square of a term.

Examples of Perfect Squares:

• Integer Examples: 1, 4, 9, 16, 25, 36, ...
• Variable Examples: x², y⁴, a⁶ (Any variable with an even exponent is a perfect square)

Difference of Squares

The difference of squares states that the difference (subtraction) between two perfect squares can be written in the following form:

a² - b² = (a - b)(a + b)

Examples:

• x² - 9 = (x - 3)(x + 3)
• 4y² - 25 = (2y - 5)(2y + 5)
• 49a² - 64b² = (7a - 8b)(7a + 8b)

Steps to Factor Using Difference of Squares:

1. Check if both terms are perfect squares.
2. Confirm that they are separated by subtraction.
3. Rewrite the expression using the formula a² - b² = (a - b)(a + b).